An efficient algorithm for nucleolus and prekernel computation in some classes of TU-games

We consider classes of TU-games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschler's scheme for approximating the prekernel. \u

Note on the game chromatic index of trees

We study edge coloring games defining the so-called game chromatic index of a graph. It has been reported that the game chromatic index of trees with maximum degree $\Delta = 3$ is at most $\Delta + 1$. We show that the same holds true in case $\Delta \geq 6$, which would leave only the cases $\Delta = 4$ and $\Delta = 5$ open. \u

Luther als protestantischer Katechet

Luther as protestant catechist Luther’s catechetical activity is based on the catechetic tradition already extant in the Early Church. He reverts to this tradition, and more especially to the catechetical instruction of the Middle Ages. Luther observed great negligence and deficiency with regard to the catechesis in the Roman Catholicism of his time. In Luther’s view, a catechism is a short summary of Holy Scrip-ture; it is a condensed and succinct expression of the teachings of the Christian faith. Along with his study on the unfree will (“De servo arbitrio”) Luther considered his two catechisms, which developed out of his preaching activity, as his most im-portant written work. His “Small catechism”, which was very well received, was reissued more than 60 times – and translated into a variety of languages – up until the time of his death. According to Luther, catechesis (catechetical instruction) is the means by which the catechism is to be learned. A vital part of this process is that the catechism must take root in the heart. The catechism is not a vehicle for objective, scientific faith, but rather defines a living, personal faith as trust in God. All Christians, including adults, must therefore know the catechism in such a way that it is engraved on their consciousness. This necessitates the attendance of catechetical sermons. There is much pneumatological profit to be had in the reading and discussion of the catechism, and in meditating on it, because the Holy Spirit is present in all these activities. All that is necessary for the Christian to know about his salvation is richly and thoroughly present in the catechism. In the light of this, the catechism is profoundly trinitarian and eschatological in orientation. The catechism teaches that the fulfilment of the Ten Commandments, the realisation of the good, is born out of true faith. Those who do not know the catechism are not allowed to partake in the sacrament of the Lord’s Supper

Some order dimension bounds for communication complexity problems

We associate with a general (0, 1)-matrixM an ordered setP(M) and derive lower and upper bounds for the deterministic communication complexity ofM in terms of the order dimension ofP(M). We furthermore consider the special class of communication matricesM obtained as cliques vs. stable sets incidence matrices of comparability graphsG. We bound their complexity byO((logd)·(logn)), wheren is the number of nodes ofG andd is the order dimension of an orientation ofG. In this special case, our bound is shown to improve other well-known bounds obtained for the general cliques vs. stable set problem

Computing an element in the lexicographic kernel of a game

The lexicographic kernel of a game lexicographically maximizes the surplusses $s_{ij}$ (rather than the excesses as would the nucleolus). We show that an element in the lexicographic kernel can be computed efficiently, provided we can efficiently compute the surplusses $s_{ij}(x)$ corresponding to a given allocation $x$. This approach improves previously obtained results and allows us to determine a kernel element without appealing to Maschler transfers in the execution of the algorithm. \u

Intercalation of graphene on SiC(0001) via ion-implantation

Electronic devices based on graphene technology are catching on rapidly and the ability to engineer graphene properties at the nanoscale is becoming, more than ever, indispensable. Here, we present a new procedure of graphene functionalization on SiC(0001) that paves the way towards the fabrication of complex graphene electronic chips. The procedure resides on the well-known ion-implantation technique. The efficiency of the working principle is demonstrated by the intercalation of the epitaxial graphene layer on SiC(0001) with Bi atoms, which was not possible following standard procedures. Our results put forward the ion-beam lithography to nanostructure and functionalize desired graphene chips

Accuracy and Precision of Near Infra-red Spectroscopy (NIRS) versus Wet Chemistry in Forage Analysis

Near Infra-red Spectroscopy (NIRS) is an attractive option for forage analysis. NIRS is less labor intensive, nondestructive, rapid, environmentally friendly and provides accurate and precise results. However, many nutritionists are quick to brush off NIRS, citing ‘poor accuracy’. We evaluated the accuracy and precision of dry matter (DM), crude protein (CP), acid detergent fiber (ADF), and neutral detergent fiber (NDF) of 33 National Forage Testing Association (NFTA) proficiency test (PT) alfalfa hay samples analyzed by NIRS in 7 NIRS Forage and Feed Testing Consortium (NIRSC) member laboratories. The reference method averages (RMA), used to evaluate the NIRS results, were based on the wet chemistry results reported by numerous laboratories participating in the corresponding NFTA proficiency testing rounds. Thus, this study is a robust comparison of NIRS determined results with the corresponding wet chemistry results, which is still a “gold standard” to many nutritionists. These results demonstrate that when NIRS calibrations are developed using good science and applied properly, NIRS is as accurate as wet chemistry in forage nutritional analysis. Further, both intra-laboratory and inter-laboratory precision of NIRS methods are superior to wet chemistry method

Can treatment success with 5% lidocaine medicated plaster be predicted in cancer pain with neuropathic components or trigeminal neuropathic pain?

An expert group of 40 pain specialists from 16 countries performed a first assessment of the value of predictors for treatment success with 5% lidocaine-medicated plaster in the management of cancer pain with neuropathic components and trigeminal neuropathic pain. Results were based on the retrospective analysis of 68 case reports (sent in by participants in the 4 weeks prior to the conference) and the practical experience of the experts. Lidocaine plaster treatment was mostly successful for surgery or chemotherapy-related cancer pain with neuropathic components. A dose reduction of systemic pain treatment was observed in at least 50% of all cancer pain patients using the plaster as adjunct treatment; the presence of allodynia, hyperalgesia or pain quality provided a potential but not definitively clear indication of treatment success. In trigeminal neuropathic pain, continuous pain, severe allodynia, hyperalgesia, or postherpetic neuralgia or trauma as the cause of orofacial neuropathic pain were perceived as potential predictors of treatment success with lidocaine plaster. In conclusion, these findings provide a first assessment of the likelihood of treatment benefits with 5% lidocaine-medicated plaster in the management of cancer pain with neuropathic components and trigeminal neuropathic pain and support conducting large, well-designed multicenter studies

The Least-core and Nucleolus of Path Cooperative Games

Cooperative games provide an appropriate framework for fair and stable profit distribution in multiagent systems. In this paper, we study the algorithmic issues on path cooperative games that arise from the situations where some commodity flows through a network. In these games, a coalition of edges or vertices is successful if it enables a path from the source to the sink in the network, and lose otherwise. Based on dual theory of linear programming and the relationship with flow games, we provide the characterizations on the CS-core, least-core and nucleolus of path cooperative games. Furthermore, we show that the least-core and nucleolus are polynomially solvable for path cooperative games defined on both directed and undirected network